Let \(q=p^h\) , where \(h\)  is a positive integer and \(p\)  is a prime.
Linearized polynomials over \({\mathbb {F}}_{q^n}\) 
correspond to \({\mathbb {F}}_q\) -linear transformations of the \(n\) -dimensional \({\mathbb {F}}_q\) -vector space \({\mathbb {F}}_{q^n}\) .
For this reason they have been intensively investigated and used to describe geometric and algebraic objects such as rank metric codes, \({\mathbb {F}}_q\) -linear sets, see e.g. [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}.
